Representations of pseudo Vitali spaces and Loomis-Sikorski theorem

A. Dvurecenskij; F. Ventriglia

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Representations of pseudo Vitali spaces and Loomis-Sikorski theorem

机译：伪维塔利空间和Loomis-Sikorski定理的表示

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We present pseudo Vitali spaces as lattices with a partially defined operation, +, that is not necessarily commutative. We show that they can be embedded into -e-groups, and we give a categorical equivalence of the category of pseudo Vitali spaces. Studying states on Vitali spaces with strong unit, we show that every Dedekind σ-complete Vitali space is an epimorphic image of a Vitali space of bounded functions where the operations on functions are defined pointwise.

机译：我们将伪维塔利空间表示为具有部分定义的运算+的格，该运算不一定是可交换的。我们证明了它们可以嵌入到-e-groups中，并且给出了伪Vitali空间类别的分类等价性。研究具有强单位的Vitali空间上的状态，我们发现每个Dedekindσ-完全Vitali空间都是有界函数的Vitali空间的上胚图像，其中对函数的操作是逐点定义的。

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来源
《International journal of general systems》 |2011年第1期|p.39-59|共21页
作者
A. Dvurecenskij; F. Ventriglia;
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作者单位

Mathematical Institute, Slovak Academy of Sciences, Stefdnikova 49, SK-814 73 Bratislava, Slovakia;

Department of Mathematics and Applications ('R. Caccioppoli'), University of Naples ('Federico IF), Complex Monte S. Angelo, Via Cintia, I-801 26 Naples, Italy;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
pseudo vitali space; state; ?-group; loomis-sikorski theorem; g-vitali space;

机译：假生命空间;州;？-组;loomis-sikorski定理;g维他命空间;

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2. Radon-Nikodym theorem and Vitali-Hahn-Saks theorem on fuzzy number measures in Banach spacers [J] . Jianrong Wu, Xiaoping Xue, Congxin Wu Fuzzy sets and systems . 2001,第3期

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3. Some fixed point theorems in compact spaces and pseudo-compact Tichonov spaces [J] . V. B. Dhagat, A. Sharma, R. Bhardwaj International journal of mathematical analysis . 2008,第9a12期

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4. Strong convergence theorems for k-strictly pseudo-contractive mapping in Hilbert spaces [C] . Qiuxia Lu, Yan Hao International Conference on Mechatronics and Information Technology . 2016

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6. ON THE VITALI-HAHN-SAKS AND NIKODÝM THEOREMS [O] . James K. Brooks 2016

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Representations of pseudo Vitali spaces and Loomis-Sikorski theorem

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